Poisson Distribution question on the odds of something happening if the time interval changes

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Given an event X that has a 68% chance of happening within 3 years, what are the odds of that event happening each year?

I tried to solve this using a Poisson Distribution but I am confused how my time interval factors into the equation.

I used the equation ((e ^ -lambda) * (lambda ^ # of successes)) / (# of successes)! = P(x) where lambda represents the expected number of successes.